The complete mixability and convex minimization problems with monotone marginal densities

@article{Wang2011TheCM,
  title={The complete mixability and convex minimization problems with monotone marginal densities},
  author={Bin Wang and Ruodu Wang},
  journal={J. Multivariate Analysis},
  year={2011},
  volume={102},
  pages={1344-1360}
}
Following the results of Ruschendorf and Uckelmann (2002) [20], we introduce the completely mixable distributions on R and prove that the distributions with monotone density and moderate mean are completely mixable. Using this method, we solve the minimization problem min"X"""i"~"PEf(X"1+...+X"n) for convex functions f and marginal distributions P with monotone density. Our results also provide valuable implications in variance minimization, bounds for the sum of random variables and risk… CONTINUE READING

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